{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 05\n",
    "\n",
    "# 参数方程\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ccc6dd2-1550-455e-b71d-81127bc3bb84",
   "metadata": {},
   "source": [
    "这段代码使用SymPy库绘制了单位圆的参数曲线，通过给定的参数方程生成一个半径为1、中心在原点的圆。具体步骤如下：\n",
    "\n",
    "1. **定义符号变量和参数方程**：使用$t$作为参数变量，定义单位圆的$x$和$y$坐标为：\n",
    "   $$ \n",
    "   x = \\cos(t) \n",
    "   $$\n",
    "   $$\n",
    "   y = \\sin(t) \n",
    "   $$\n",
    "   其中，$t$的取值范围为$[0, 2\\pi]$。这两个方程表示一个以原点为圆心、半径为1的单位圆。随着$t$从$0$到$2\\pi$变化，圆周上的所有点被依次生成。\n",
    "\n",
    "2. **绘制参数曲线**：调用$plot\\_parametric$函数绘制单位圆。参数范围设置为$t \\in [0, 2\\pi]$，表示从起点$(1, 0)$开始，按逆时针方向绘制完整的圆。图形大小设定为$10 \\times 10$，以确保圆形在图形窗口中对称显示。\n",
    "\n",
    "通过SymPy的符号计算和绘图功能，这段代码展示了如何用参数方程生成单位圆，并在极坐标系中使用参数化的方法来表达和展示几何图形。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f50c709-14ec-40f1-8472-a80dd6793c5d",
   "metadata": {},
   "source": [
    "## 导入所需库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "11b443a0-9773-4410-a9b1-7d3e8536a81a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *  # 导入sympy库，用于符号计算\n",
    "from sympy.plotting import plot_parametric  # 导入sympy的参数绘图模块\n",
    "import math  # 导入math库，用于数学常数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6283e29b-1835-4e29-92f5-3264fb32ed3f",
   "metadata": {},
   "source": [
    "## 定义符号变量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0bb32bff-d895-454f-a0b0-957cd9aed1a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = symbols('t')  # 定义参数变量t，用于参数方程"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09b9c759-78b2-40ce-94ec-dc2ef6478d20",
   "metadata": {},
   "source": [
    "## 单位圆的参数方程"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1a2dc174-69d8-41b9-921d-7037f6379abd",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = cos(t)  # 定义单位圆的x坐标，使用cos函数\n",
    "x2 = sin(t)  # 定义单位圆的y坐标，使用sin函数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4ce01ab-5e5c-4d8c-9aae-abcdd46d1b7b",
   "metadata": {},
   "source": [
    "## 绘制单位圆"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "28ee762d-b201-40df-b728-8f6f9b545d53",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.backends.matplotlibbackend.matplotlib.MatplotlibBackend at 0x21f23f64260>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_parametric(x1, x2, (t, 0, 2 * pi), size=(10, 10))  # 绘制单位圆，参数范围为t从0到2π，图形大小为10x10"
   ]
  }
 ],
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